Question

Edit – Rewrote question since the original did not makes sense:

In R – how would I go about getting a lm fit model that is a quotient of sums for two variables grouped by a third factor variable, but that weights some entries more than others? Data looks like:

Browser       Visits    Clicks
Chrome         100       25
Chrome         89        40
Chrome         10        0
Safari         40        10
Safari         30        2    

From the comments this is the command for the WLS regression weighted by visits, but I don’t think I’m using the weight function right since I don’t know how the errors are correlated with visits, just that they are.

fit <- lm(Clicks/Visits ~ Browser, weights=(visits/sum(visits)))

Answer 1

You are asking for a rate model, i.e. events per number at risk. This is usually implemented by modeling the process as a Poisson distributed set of events:

    dat <- read.table(textConnection("Browser       Visits    Clicks
 Chrome         100       25
 Chrome         89        40
 Chrome         10        0
 Safari         40        10
 Safari         30        2"), header=TRUE)

 dat$CperV <- with(dat, Clicks/Visits)
    dat


 glm(CperV ~ Browser, data=dat, family = "poisson")

Call:  glm(formula = CperV ~ Browser, family = "poisson", data = dat)

Coefficients:
  (Intercept)  BrowserSafari  
       -1.456         -0.387  

Degrees of Freedom: 4 Total (i.e. Null);  3 Residual
Null Deviance:      0.772 
Residual Deviance: 0.7379   AIC: Inf 
    Residual Deviance: 0.1182   AIC: 1.467 

> exp(-1.456  ) # estimated rate for nonSafari Visits
[1] 0.2331671
> exp(-1.456-0.387 ) # estimated rate for Safari Visits
[1] 0.1583417
> mean(dat[dat$Browser=="Safari",  "CperV"])  # actual means
[1] 0.1583333
> mean(dat[dat$Browser!="Safari",  "CperV"])  # actual means
[1] 0.2331461